That's interesting. I didn't think an extension could change the search engines available under Settings > Safari > Search Engine on iOS from the defaults (Google, Bing, Yahoo, DDG, Ecosia), or change the system-wide search used. Do you see different options now under Settings for search engines and did it change your system-wide search too (i.e. swipe down on home screen and then use the built-in Search)?
Swiping down doesn’t work, it’s in-browser only in the address bar. As for in safari, I don’t get options, but if the extension is enabled it redirects the search to Kagi.